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An Introduction to Sato's Hyperfunctions
Mitsuo Morimoto, Sophia University, Tokyo, Japan
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Translations of Mathematical Monographs
1993; 273 pp; hardcover
Volume: 129
ISBN-10: 0-8218-4571-3
ISBN-13: 978-0-8218-4571-4
List Price: US$112
Member Price: US$89.60
Order Code: MMONO/129
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This book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research.

Readership

Graduate students and research mathematicians.

Reviews

"Many concrete examples illustrate the theory and make the book a valuable text for beginners."

-- Zentralblatt MATH

"Morimoto's classical approach is ... valuable ... as a necessary complement to more abstract presentations of the subject"

-- Mathematical Reviews

Table of Contents

  • Fundamental properties of holomorphic functions
  • Analytic functionals of one variable
  • Hyperfunctions of one variable
  • Cohomology groups with coefficients in a sheaf
  • Cohomology groups with coefficients in \({\mathcal O}\)
  • Analytic functionals of several variables
  • Hyperfunctions of several variables
  • Microfunctions
  • Development of hyperfunction theory
  • Appendix A. Linear topological spaces
  • Appendix B. Rudiments of homological algebra
  • Appendix C. Bibliographical notes
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